EXPLANATION:
Given;
We are given two ice cream cups in the shapes of a cone and a cylinder.
The dimensions are;
[tex]\begin{gathered} Cone: \\ Radius=4in \\ \\ Height=6in \\ \\ Cylinder: \\ Radius=3in \\ \\ Height=2in \end{gathered}[/tex]Required;
We are required to determine which of the two cups will hold the most ice cream.
Step-by-step solution;
Take note that the radius of the cylinder was derived as follows;
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \\ radius=\frac{6}{2}=3 \end{gathered}[/tex]The volume of the cone is given by the formula;
[tex]\begin{gathered} Volume=\frac{1}{3}\pi r^2h \\ \\ Therefore: \\ Volume=\frac{1}{3}\times3.14\times4^2\times6 \\ \\ Volume=\frac{3.14\times16\times6}{3} \\ \\ Volume=100.48 \end{gathered}[/tex]Rounded to the nearest tenth, the volume that the cone can hold will be;
[tex]Vol_{cone}=100.5in^3[/tex]Also, the volume of the cylinder is given by the formula;
[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=3.14\times3^2\times2 \\ \\ Volume=3.14\times9\times2 \\ \\ Volume=56.52 \end{gathered}[/tex]Rounded to the nearest tenth, the volume will be;
[tex]Vol_{cylinder}=56.5in^3[/tex]ANSWER:
Therefore, the results show that the CONE will hold the most ice cream.
